Force & MotionForce & Motion

Dynamics Dynamics

how things movehow things move

Believed everything moved to return to its Believed everything moved to return to its own. ie. rock to earth, smoke to airown. ie. rock to earth, smoke to air

Objects want to be in a state of rest.Objects want to be in a state of rest.

Galileo (15-1600 AD)Galileo (15-1600 AD)Dropped objects from the Leaning Tower of Dropped objects from the Leaning Tower of Pisa. Too quick, Too Fast Pisa. Too quick, Too Fast after 3s, v = after 3s, v = 29 m/s (64 mi/hr), y = 44 m (1/2 football 29 m/s (64 mi/hr), y = 44 m (1/2 football field) per secondfield) per second

Aristotle (4-300 BC)

?

Slowed things down by rolling balls down various inclines.

It always came to about the same height.

What would happen on a smooth horizontal surface?

Inertia tendency of an object to maintain a state of rest or motion

Newton (16-1700 AD)Newton (16-1700 AD)

Mass is a measure of inertiaMass is a measure of inertia

The more mass you have, the less it wants The more mass you have, the less it wants to change its state of motion.to change its state of motion.

11stst Law (Law of Inertia) Law (Law of Inertia)

An object in motion tends to stay in An object in motion tends to stay in motion with a constant velocity and an motion with a constant velocity and an object at rest tends to stay at rest, unless object at rest tends to stay at rest, unless

acted on by an unbalanced force. acted on by an unbalanced force.

ForceForce

a push or pull on an object a push or pull on an object

(measured in Newtons)(measured in Newtons)

Net Force (FNet Force (Fnetnet))

is the sum of all the forces acting on is the sum of all the forces acting on an objectan object

Balanced Unbalanced

F2 = -2 NF1 = 2 N

Fnet = 2 + -2 = 0 N

F2 = -5 NF1 = 2 N

Fnet = 2 + -5 = -3 N

Force Diagrams (Free Body Diagram) a vector diagram of all the forces acting on a vector diagram of all the forces acting on an object an object1. Draw the object as a single dot.

2. Draw the force vectors as coming out of the dot. Label each of the vectors.F1 Force of object 1 on object 2

3. Check to make sure that all forces are accounted for.

2 Types of forcesContact – Look at the objects actually touchingNoncontact – look at gravity, electricity, and magnetism

Normal Force force perpendicular to the ground pushing up

Draw a force diagram of you sitting in your desk.

Accelerating out of the parking lot, you put your foot on the gas and the engine applies 2500 N of force forward on your 10,000 N car. If the ground puts 1000 N of friction back on the car:a. draw a free body diagram

b. what is the net force?

Samples

Newton’s 2Newton’s 2ndnd Law LawIf all objects resting want to stay resting, If all objects resting want to stay resting,

how do they move?how do they move?If all objects moving want to stay moving, If all objects moving want to stay moving,

how do they stop?how do they stop?Force!!!Force!!!

F ↑ a ↑F α a Force is directly proportional to accel.

m ↓ a ↑1/m α a mass is inversely proportional to accel.

2nd Law (Law of Acceleration)Force makes an object want to accelerate.Mass makes an object not want to accelerate.

a α Fnet/m a = k Fnet / m Const = 1a = F/mF = ma

1 Newton = amount of force necessary to accelerate a 1 kg mass at 1 m/s2

1 N = 1 kg m/s2

This would be like holding 100 g in your hand. 1 N = (.1 kg) (9.8m/s2)

1lb is about 4 N

Net force in the Net force in the y direction y direction usually cancels usually cancels out to zero:out to zero:

FN

Fg

FyouFF

FN

Fg

Fyou

FF

FyouX

FyouY

No AngleFnety = 0

FN – Fg = 0 FN = Fg

AngleFnety = 0

FN + Fy = Fg

AcceleratingFnetx = ma

Fx – Ff = ma

Constant VelocityFnetx = 0

Fx – Ff = 0Fx = Ff

Net force in x direction causes acceleration:

196 NF2 = -5 NF1 = 2 N

Fnet = 2 + -5 = -3 N

F = ma

-3 = 20 aa = -0.15 m/s2

196 N= m (9.8 m/s2)m = 20 kg

Weight force of gravityF = maFg = m g

To find the mass, take the weight, divide by 9.8.

Use vf, x, or t to find a, then a to find Fnet, or use Fnet to find a then a to find vf, x, or t

Fneta

vf

xtvi

Fnet = max = vit + ½ at2

vf = vi + atvf

2 = vi2 + 2ax

You pull a 50 N block with a force of 15 N at You pull a 50 N block with a force of 15 N at 2626°.°.a. draw a force diagrama. draw a force diagramb. find the mass of the block.b. find the mass of the block.c. find the components of your force.c. find the components of your force.d. find the normal forced. find the normal forcee. find the acceleration of the block if friction e. find the acceleration of the block if friction is 4 N?is 4 N?f. find the block’s final velocity after 3 s?f. find the block’s final velocity after 3 s?

X directionFnet = m aFx = 5.10 a13.5 -4 = 5.10 aa = 1.86 m/s2

Givensvi = 0a = 1.86 m/s2

t = 3 svf = ?vf = vi + atvf = 0 + (1.86)(3)vf = 5.59 m/s

Fg = m g50 = m(9.8)m = 5.10 kg

15 NFx = 15 cos 26 = 13.5 NFy = 15 sin 26 = 6.58 N

FN

Y directionFnet = m aFnet = 0 FN + Fy – Fg = 0FN + 6.58 – 50 = 0FN = 43.4 N

13.5 N6.58 N

Fg = m a

Newton’s Third LawNewton’s Third Law

Newton’s 3Newton’s 3rdrd Law Law

Every Action has an equal and opposite reaction.Every Action has an equal and opposite reaction.

Every interaction happens in 2’s. Every interaction happens in 2’s. Action Force and Reaction ForceAction Force and Reaction Force

How do we know what action & reaction are?How do we know what action & reaction are?

Action: Object A exerts a force on object BAction: Object A exerts a force on object B

Reaction: Object B exerts a force on object AReaction: Object B exerts a force on object A

Notice that these forces are acting on two different objects.

example: Earth exerts a force on BoulderBoulder exerts a force on Earth

If the boulder exerts a force on the earth that is equal, why doesn’t the earth accelerate to the

boulder?

Force of Earth on Boulder

Force of Boulder on Earth

Mass! 2Mass! 2ndnd Law!!! Law!!!

F = FF = F

m m AA = = MM a a

So the earth moves, but it is soooo small that we So the earth moves, but it is soooo small that we can’t tell!can’t tell!

Another example… horse and cart.Another example… horse and cart.

Are the equal and opposite forces acting on the Are the equal and opposite forces acting on the same object?same object?